On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators

In present paper the classes of nonlinear integral equations with non completely continuous operators are considered.
It is assumed that conservative nonlinear operator of Wiener–Hopf-Hankell–Hammerstein type is a linear minorant to the initial Urysohn operator. The alternative theorems of the existence of positive solutions of above-mentioned class equations are proved. The asymptotic behavior of the obtained solutions at infinity is investigated. The article is finalized by the presentation of some examples arising in applications.